Sub-band coding refers to a technique where, by the parallel application of a set of filters, an input signal is decomposed into several narrow bands that are separately decimated and coded for the purpose of transmission. For reconstruction after tranmission, the individual bands are decoded, interpolated and filtered in order to reproduce the original signal. Originally, sub-band coding was developed in connection with the coding and transmission of speech signals. (See e.g. R. E. Crochiere et al. "Digital Coding of Speech in Sub-bands", BSTJ Vol. 55, pp. 1069-1085.)
In the case of a video signal, separable filter banks are applied first horizontally then vertically. Application of a filter bank comprising two filters, first horizontally then vertically, gives rise to an analysis of a video signal in four frequency bands: horizontal low-vertical low; horizontal low-vertical high; horizontal high-vertical low; horizontal high-vertical high. Each resulting band is encoded according to its own statistics for transmission from a coding station to a receiving station.
A very important part of the design of a sub-band code is the choice of the analysis and synthesis filter banks that are used to decompose and reconstruct the original video signal. Much of the design work in filter banks has been motivated by speech processing where sharp band separation is a very desirable property. This work led naturally to finite impulse response (FIR) filter banks with a very large number of stages, e.g. 64. A classical approach to designing such filters is the Quadrature Mirror Filter approach which, in the absence of channel and quantization noise, permits an alias free and near perfect reconstruction of the input signal when the input signal is a one-dimensional speech signal (see. e.g. D. Esteban et al., "Application of Quadrature Mirror Filters to Split Band Voice Coding Schemes", Proc 1977 Int'l IEEE Conf. on ASSP, pp. 191-195). Application of the Quadrature Mirror concept to the sub-band coding of digital images has recently received considerable attention, and the technique has been shown to be highly effective for image compression. (See e.g., M. Vetterli, "Multi-dimensional Sub-band Coding: Some Theory and Algorithms," Signal Processing 6 (1984), pp. 97-112; J. W. Woods and S. O'Neil, "Sub-Band Coding of Images," Proc. ICASSP 86, pp. 1005-1008, April 1986; H. Gharavi, and A. Tabatabai, "Sub-band Coding of Digital Images Using Two-Dimensional Quadrature Mirror Filter," Proc. SPIE, vol. 707, pp. 51-61, September 1986; J. W. Woods and S. D. O'Neil, "Subband Coding of Images," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 1278-1288, October 1986; H. Gharavi and A. Tabatabai, "Application of Quadrature Mirror Filtering to the Coding of Monochrome and Color Images," Proc. ICASSP 87, vol. 4, pp. 2384-2387; P. H. Westerink, J. Biemond and D. E. Boekee, "Sub-Band Coding of Digital Images Using Predictive Vector Quantization," Proc. ICASSP 87, vol. 3, pp. 1378-1381).
A disadvantage of the classical Quadrature Mirror Approach is that for video signals, the resulting filters do not permit reconstruction of the original video signal to be exact, although amplitude distortion can be made small by using long, multiple stage filters. In addition, use of the long, multiple stage filters provided by the Quadrature Mirror Approach does not provide any significant coding gains and substantially increases hardware complexity. A variety of other filters have been proposed for the sub-band coding of signals (see e.g., M. Smith et al., "Exact Reconstruction Techniques for Tree Structured Subband Codes," IEEE Trans Account, Speech, Signal Processing, vol. ASSP-34, pp. 434-441, June 1986 and M. Vetterli, "Filter Bands Allowing Perfect Reconstruction", Signal Processing, vol. 10, No. 3, pp. 219-244, April 1986). However, these filters have not proven entirely satisfactory for video sub-band coding applications.
Accordingly, it is an object of the present invention to provide filter banks for use in the sub-band coding of video and image signals, which banks comprise filters of short and simple design so that an original signal can be analyzed and synthesized with minimal computational complexity and so that the original signal can be exactly reconstructed without aliasing effects.